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and 02 Let T : R2 + RP be the linear transformation satisfying 9 5 Tū1)...
(1 point) Let in = [] and v2 = [:3] Let T : R2 + R2 be the linear transformation satisfying TW) = ( 13 ) and Tlőz) = 1 3 х Find the image of an arbitrary vector -(:) -
Let t be the linear transformation t: r2 -> r2 that reflects a vector about the line y=x. Find the eigenvalue and eigenvectors of T. How can you interpret this geometrically?
Verify that a linear transformation T from R2 into R2 Q1: Verify that a linear transformation T from RP into R T(V1, V2) = (v1 – V2, V1 + 2v2)
5. Let T: P2(R) + RP be the linear transformation that has the matrix …_…………..ນະ 1 2 -1 11 1 1 relative to the bases a = 1+ 21,1+1+12,1+for P2 (R) and B = (1,1),(1,-1) for R2. Find the matrix of T relative to the bases d' = 2+3.r,1+1+12,2+3.+r2 for P2(R) and B' =(3,-1),(1,-1) for R2.
13. Let L : R2 → R2 be the linear transformation satisfying L(111) 1 , and L(1-11) A. B. D. E.
1. (10 points) Let T:P3 → P3 be the linear transformation satisfying T(x2 - 1) = x² + x - 3, T(2x) = 4x, and T(3x + 2) = 2(x + 3). Determine T(ax+ bx + c), where a, b, and c are arbitrary real numbers.
linear algebra Let T: R2 R2 be a reflection in the line y = -x. Find the image of each vector. (a) (-3,9) (b) (5, -1) (c) (a,0) (d) (o, b) (e) ( ed) (f) (9)
1. (10 points) Let T:P3 → P3 be the linear transformation satisfying T(x2 - 1) = x2 + x-3, T(2x) = 4x, and T(3x + 2) = 2(x + 3). Determine T(ax? + bx + c), where a, b, and c are arbitrary real numbers.
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
4.10. Let T be a linear transformation on a vector space V satisfying T-T2 = id. Show that T is invertible.